Data Analysis for The effects of visual cues on understanding classification in immersive scatterplots
2020-12-23
Dependencies
library(ggplot2) #core graphics package
library(ggridges) # ggarrange
library(ggpubr)
library(ggdist)
library(ggtext)
library(tidyverse) # data manipulation
library(rstan) #detectCores
library(brms) # core pack
library(parallel) #detectCores
library(tidybayes)
REBUILD_FLAG <<- FALSELoad data
metas <- read.csv("../data/metas.csv", stringsAsFactors = F, header = T)
trials_all <- read.csv("../data/trials.csv", stringsAsFactors = F, header = T)
seper <- " o "
trials_all <- trials_all %>%
filter(TrialStatus == "main") %>% #drop practice trial
mutate(Error = TrialAnswer - TrialIntAccuracy,
ErrorMagnitude = abs(Error),
ResponseTime = (TrialVisualizationEnd - TrialVisualizationStart) / 1000,
LogResponseTime = log(ResponseTime)) %>% # log transform
filter(!(ParticipantID == "P7" & SessionIndex == 0 & TrialStatus == "main" & TrialIndex == 16)) %>% # filter mistakes
filter(!(ParticipantID == "P9" & SessionIndex == 2 & TrialStatus == "main" & TrialIndex == 17)) %>%
filter(!(ParticipantID == "P11" & SessionIndex == 0 & TrialStatus == "main" & TrialIndex == 12)) %>%
filter(!(ParticipantID == "P20" & SessionIndex == 3 & TrialStatus == "main" & TrialIndex == 5)) %>%
filter(!(ParticipantID == "P24" & SessionIndex == 0 & TrialStatus == "main" & TrialIndex == 26)) %>%
filter(ErrorMagnitude < 51) %>%
mutate( # manual recode levels using orthogonal contrast coding
AllFactors = paste(FactorStereo, FactorMotion, FactorPerspective, FactorShading, Dim, sep = seper),
Stereo = recode(FactorStereo, yes = 0.5, no = -0.5),
Motion = recode(FactorMotion, yes = 0.5, no = -0.5),
Perspective = recode(FactorPerspective, yes = 0.5, no = -0.5),
Shading = recode(FactorShading, `shading-1` = 0, `shading-2` = 0.5, `flat`= -0.5, `no` = -0.5),
Dataset = recode(TrialDataset, "cifar10" = 0.5, "babi-q1" = -0.5),
Dimension = recode(Dim, `2` = -0.5, `3` = 0.5)
)
trials <- trials_all %>%
select(ParticipantID, ErrorMagnitude, ResponseTime, Stereo, Motion, Perspective, Shading, Dimension, Dataset)
vtrials <- trials_all %>%
select(ParticipantID, ErrorMagnitude, ResponseTime, FactorStereo, FactorMotion, FactorPerspective, FactorShading, Dim, TrialDataset, AllFactors)Raw data
We first plot all raw data to get a sense of how data distribute. Both error magnitude and response time datum seem not to follow a normal distribution, and they are both non-negative. A skewed normal, lognormal, and gamma distribution could be reasonable. Note that error magnitude contains 0, and response time has a upper bound 60s (e.g., 60.1s, 60.2s due to running time). We will use gamma distribution for both measures. To formally compare which
g_raw_error <- vtrials %>%
ggplot(mapping = aes(x = ErrorMagnitude)) +
facet_wrap(AllFactors ~ .,ncol = 3, scales = "free") +
coord_cartesian(xlim = c(0, 50), ylim = c(0, 30)) +
geom_histogram(binwidth = 2, fill = "lightblue", color = "white") +
ggtitle("raw data - error magnitude (%)") +
xlab ("error magnitude ") + ylab("count")
g_raw_error
ggsave(g_raw_error, filename = "pic/g_raw_error.pdf", width = 10, height = 10, units = "in")
g_raw_time <- vtrials %>%
ggplot(mapping = aes(x = ResponseTime)) +
facet_wrap(AllFactors ~ .,ncol = 3, scales = "free") +
coord_cartesian(xlim = c(0, 62), ylim = c(0, 30)) +
geom_histogram(binwidth = 2, fill = "lightgray", color = "white") +
ggtitle("raw data - response time (s)") +
xlab ("response time ") + ylab("count")
g_raw_time
ggsave(g_raw_time, filename = "pic/g_raw_time.pdf", width = 10, height = 10, units = "in")helper function for model diagnostics
model_diagnostics <- function(m, name = "model diagnostics"){
print(name)
print(summary(m))
# plot(m)
plot(pp_check(m, type = "dens_overlay", nsamples = 100))
plot(pp_check(m, type = "stat_2d", nsamples = 100))
plot(pp_check(m, type = "error_binned", nsamples = 100))
print(loo(m))
print(waic(m))
}
# Valid types are:
# 'bars', 'bars_grouped', 'boxplot', 'data', 'dens', 'dens_overlay', 'ecdf_overlay', 'error_binned', 'error_hist', 'error_hist_grouped', 'error_scatter', 'error_scatter_avg', 'error_scatter_avg_vs_x', 'freqpoly', 'freqpoly_grouped', 'hist', 'intervals', 'intervals_data', 'intervals_grouped', 'loo_intervals', 'loo_pit', 'loo_pit_overlay', 'loo_pit_qq', 'loo_ribbon', 'ribbon', 'ribbon_data', 'ribbon_grouped', 'rootogram', 'scatter', 'scatter_avg', 'scatter_avg_grouped', 'stat', 'stat_2d', 'stat_freqpoly_grouped', 'stat_grouped', 'violin_grouped'if(REBUILD_FLAG){
m_error_hurdle_gamma <- bf(ErrorMagnitude ~
0 + Intercept +
Stereo*Motion*Perspective*Shading*Dataset +
Stereo*Dataset*Dimension +
(1 + Dimension | ParticipantID),
family = hurdle_gamma(link = "identity")
)
get_prior(m_error_hurdle_gamma, data = trials)
m_brms_error_hurdle_gamma <<- brm(m_error_hurdle_gamma,
data = trials,
family = hurdle_gamma(link = "log"),
prior = c(
prior(normal(0, 2.5), class = "b"),
prior(normal(0, 25), class = "b", coef = "Intercept"),
prior(gamma(1, 10), class = "shape"),
prior(student_t(3, 0, 5), class = "sd")
),
chains = N_CHAINS, iter = N_ITER, warmup = N_WARMUP, thin = N_THIN, cores = N_CORES,
control = list(adapt_delta = DELTA, max_treedepth = TREE_DEPTH))
saveRDS(file = "rds/m_brms_error_hurdle_gamma.rds", m_brms_error_hurdle_gamma)
}else{
m_brms_error_hurdle_gamma <<- readRDS("rds/m_brms_error_hurdle_gamma.rds")
}
model_diagnostics(m_brms_error_hurdle_gamma)## [1] "model diagnostics"
## Family: hurdle_gamma
## Links: mu = log; shape = identity; hu = identity
## Formula: ErrorMagnitude ~ 0 + Intercept + Stereo * Motion * Perspective * Shading * Dataset + Stereo * Dataset * Dimension + (1 + Dimension | ParticipantID)
## Data: trials (Number of observations: 3320)
## Samples: 2 chains, each with iter = 4000; warmup = 2000; thin = 1;
## total post-warmup samples = 4000
##
## Group-Level Effects:
## ~ParticipantID (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 0.20 0.04 0.13 0.29 1.00 1542
## sd(Dimension) 0.13 0.08 0.01 0.32 1.00 548
## cor(Intercept,Dimension) 0.18 0.45 -0.71 0.96 1.00 1945
## Tail_ESS
## sd(Intercept) 2254
## sd(Dimension) 1055
## cor(Intercept,Dimension) 1524
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept 1.96 0.05 1.86 2.06
## Stereo -0.03 0.07 -0.17 0.10
## Motion -0.03 0.03 -0.09 0.03
## Perspective 0.01 0.03 -0.05 0.07
## Shading -0.04 0.04 -0.11 0.03
## Dataset 0.06 0.07 -0.08 0.20
## Dimension 0.05 0.07 -0.09 0.20
## Stereo:Motion 0.10 0.06 -0.02 0.22
## Stereo:Perspective -0.03 0.06 -0.15 0.09
## Motion:Perspective -0.04 0.06 -0.16 0.07
## Stereo:Shading -0.00 0.07 -0.15 0.14
## Motion:Shading 0.06 0.07 -0.08 0.21
## Perspective:Shading 0.03 0.07 -0.11 0.17
## Stereo:Dataset 0.13 0.14 -0.15 0.42
## Motion:Dataset -0.11 0.08 -0.27 0.04
## Perspective:Dataset 0.07 0.06 -0.05 0.19
## Shading:Dataset 0.00 0.07 -0.13 0.14
## Stereo:Dimension 0.13 0.14 -0.14 0.40
## Dataset:Dimension 0.11 0.14 -0.16 0.39
## Stereo:Motion:Perspective 0.09 0.12 -0.15 0.32
## Stereo:Motion:Shading 0.15 0.14 -0.13 0.42
## Stereo:Perspective:Shading 0.23 0.14 -0.06 0.51
## Motion:Perspective:Shading 0.03 0.15 -0.26 0.31
## Stereo:Motion:Dataset 0.12 0.16 -0.19 0.44
## Stereo:Perspective:Dataset 0.15 0.12 -0.07 0.39
## Motion:Perspective:Dataset 0.02 0.12 -0.21 0.25
## Stereo:Shading:Dataset 0.08 0.15 -0.21 0.37
## Motion:Shading:Dataset 0.30 0.14 0.02 0.58
## Perspective:Shading:Dataset -0.08 0.14 -0.36 0.21
## Stereo:Dataset:Dimension -0.21 0.29 -0.77 0.35
## Stereo:Motion:Perspective:Shading 0.11 0.28 -0.43 0.66
## Stereo:Motion:Perspective:Dataset -0.08 0.24 -0.56 0.38
## Stereo:Motion:Shading:Dataset 0.28 0.29 -0.28 0.83
## Stereo:Perspective:Shading:Dataset -0.01 0.29 -0.58 0.56
## Motion:Perspective:Shading:Dataset 0.34 0.29 -0.23 0.91
## Stereo:Motion:Perspective:Shading:Dataset -0.39 0.57 -1.52 0.74
## Rhat Bulk_ESS Tail_ESS
## Intercept 1.00 1653 2140
## Stereo 1.00 2732 2683
## Motion 1.00 5316 3176
## Perspective 1.00 5212 3062
## Shading 1.00 4335 2956
## Dataset 1.00 2731 2413
## Dimension 1.00 3814 3064
## Stereo:Motion 1.00 5224 2852
## Stereo:Perspective 1.00 4497 2730
## Motion:Perspective 1.00 4957 3034
## Stereo:Shading 1.00 5547 3077
## Motion:Shading 1.00 5531 3101
## Perspective:Shading 1.00 4795 2890
## Stereo:Dataset 1.00 3066 2820
## Motion:Dataset 1.00 3970 2321
## Perspective:Dataset 1.00 5108 2817
## Shading:Dataset 1.00 4535 3253
## Stereo:Dimension 1.00 2558 2647
## Dataset:Dimension 1.00 2749 2875
## Stereo:Motion:Perspective 1.00 4908 3258
## Stereo:Motion:Shading 1.00 4827 2927
## Stereo:Perspective:Shading 1.00 5124 2832
## Motion:Perspective:Shading 1.00 5449 3177
## Stereo:Motion:Dataset 1.00 3704 3034
## Stereo:Perspective:Dataset 1.00 5342 2920
## Motion:Perspective:Dataset 1.00 5247 3347
## Stereo:Shading:Dataset 1.00 5093 3131
## Motion:Shading:Dataset 1.00 4711 3042
## Perspective:Shading:Dataset 1.00 4890 2809
## Stereo:Dataset:Dimension 1.00 3099 2736
## Stereo:Motion:Perspective:Shading 1.00 5169 3126
## Stereo:Motion:Perspective:Dataset 1.00 5398 3292
## Stereo:Motion:Shading:Dataset 1.00 5028 2555
## Stereo:Perspective:Shading:Dataset 1.00 6034 3406
## Motion:Perspective:Shading:Dataset 1.00 4366 3316
## Stereo:Motion:Perspective:Shading:Dataset 1.00 4858 3179
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape 1.58 0.04 1.50 1.65 1.00 5576 2806
## hu 0.07 0.00 0.06 0.08 1.00 5625 2948
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
##
## Computed from 4000 by 3320 log-likelihood matrix
##
## Estimate SE
## elpd_loo -9939.7 50.9
## p_loo 73.2 3.1
## looic 19879.4 101.8
## ------
## Monte Carlo SE of elpd_loo is 0.2.
##
## Pareto k diagnostic values:
## Count Pct. Min. n_eff
## (-Inf, 0.5] (good) 3317 99.9% 922
## (0.5, 0.7] (ok) 3 0.1% 804
## (0.7, 1] (bad) 0 0.0% <NA>
## (1, Inf) (very bad) 0 0.0% <NA>
##
## All Pareto k estimates are ok (k < 0.7).
## See help('pareto-k-diagnostic') for details.
##
## Computed from 4000 by 3320 log-likelihood matrix
##
## Estimate SE
## elpd_waic -9939.2 50.9
## p_waic 72.8 3.0
## waic 19878.5 101.7
##
## 13 (0.4%) p_waic estimates greater than 0.4. We recommend trying loo instead.if(REBUILD_FLAG == TRUE){
trials <- trials %>%
mutate(cen = ifelse(ResponseTime > 60, "left", "none"))
m_time_gamma_motion <- bf(ResponseTime | cens(cen) ~
0 + Intercept +
Stereo*Motion*Perspective*Shading*Dataset +
Stereo*Dataset*Dimension +
(1 + Motion | ParticipantID),
shape ~ 0 + Intercept + Motion,
family = Gamma(link="log")
)
priors_time_gamma_motion <- c(
set_prior("normal(0, 2.5)", class = "b"),
set_prior("normal(0, 30)", class = "b", coef = "Intercept"),
#prior(gamma(1, 20), class = "shape"),
set_prior("student_t(3, 0, 10)", class = "sd")
)
m_brms_time_gamma_motion <<- brm(m_time_gamma_motion,
data = trials, family = Gamma(link="log"), prior = priors_time_gamma_motion,
chains = N_CHAINS, iter = N_ITER, warmup = N_WARMUP, thin = N_THIN, cores = N_CORES,
control = list(adapt_delta = DELTA, max_treedepth = TREE_DEPTH))
saveRDS(file = "rds/m_brms_time_gamma_motion.rds", m_brms_time_gamma_motion)
}else{
m_brms_time_gamma_motion <<- readRDS("rds/m_brms_time_gamma_motion.rds")
}
model_diagnostics(m_brms_time_gamma_motion)## [1] "model diagnostics"
## Family: gamma
## Links: mu = log; shape = log
## Formula: ResponseTime | cens(cen) ~ 0 + Intercept + Stereo * Motion * Perspective * Shading * Dataset + Stereo * Dataset * Dimension + (1 + Motion | ParticipantID)
## shape ~ 0 + Intercept + Motion
## Data: trials (Number of observations: 3320)
## Samples: 2 chains, each with iter = 4000; warmup = 2000; thin = 1;
## total post-warmup samples = 4000
##
## Group-Level Effects:
## ~ParticipantID (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 0.62 0.08 0.48 0.81 1.01 588
## sd(Motion) 0.28 0.04 0.20 0.37 1.00 1357
## cor(Intercept,Motion) -0.50 0.15 -0.75 -0.16 1.00 1400
## Tail_ESS
## sd(Intercept) 1010
## sd(Motion) 1777
## cor(Intercept,Motion) 1873
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept 2.27 0.12 2.05 2.50
## Stereo 0.37 0.05 0.27 0.47
## Motion 0.59 0.05 0.49 0.70
## Perspective 0.04 0.02 -0.00 0.08
## Shading 0.01 0.03 -0.04 0.06
## Dataset 0.17 0.05 0.07 0.27
## Dimension 0.13 0.05 0.04 0.23
## Stereo:Motion 0.38 0.04 0.30 0.46
## Stereo:Perspective 0.03 0.04 -0.05 0.11
## Motion:Perspective 0.06 0.04 -0.03 0.14
## Stereo:Shading 0.09 0.05 -0.01 0.19
## Motion:Shading 0.15 0.05 0.05 0.24
## Perspective:Shading -0.07 0.05 -0.17 0.02
## Stereo:Dataset -0.11 0.11 -0.31 0.10
## Motion:Dataset -0.01 0.06 -0.13 0.10
## Perspective:Dataset 0.03 0.04 -0.05 0.10
## Shading:Dataset 0.07 0.05 -0.03 0.17
## Stereo:Dimension -0.06 0.10 -0.26 0.15
## Dataset:Dimension 0.06 0.10 -0.14 0.25
## Stereo:Motion:Perspective -0.03 0.08 -0.19 0.14
## Stereo:Motion:Shading -0.06 0.10 -0.25 0.14
## Stereo:Perspective:Shading 0.08 0.10 -0.12 0.28
## Motion:Perspective:Shading 0.10 0.10 -0.10 0.29
## Stereo:Motion:Dataset 0.41 0.11 0.19 0.63
## Stereo:Perspective:Dataset -0.05 0.08 -0.21 0.10
## Motion:Perspective:Dataset -0.04 0.08 -0.20 0.12
## Stereo:Shading:Dataset -0.05 0.10 -0.24 0.15
## Motion:Shading:Dataset 0.05 0.10 -0.16 0.24
## Perspective:Shading:Dataset 0.01 0.10 -0.19 0.20
## Stereo:Dataset:Dimension -0.03 0.20 -0.43 0.35
## Stereo:Motion:Perspective:Shading 0.19 0.20 -0.20 0.58
## Stereo:Motion:Perspective:Dataset 0.08 0.16 -0.25 0.39
## Stereo:Motion:Shading:Dataset -0.15 0.20 -0.54 0.23
## Stereo:Perspective:Shading:Dataset -0.07 0.20 -0.47 0.32
## Motion:Perspective:Shading:Dataset 0.26 0.20 -0.14 0.66
## Stereo:Motion:Perspective:Shading:Dataset 0.26 0.39 -0.52 1.01
## shape_Intercept 1.17 0.02 1.13 1.22
## shape_Motion 0.25 0.05 0.16 0.34
## Rhat Bulk_ESS Tail_ESS
## Intercept 1.01 263 732
## Stereo 1.00 2246 2642
## Motion 1.00 874 1758
## Perspective 1.00 5648 2768
## Shading 1.00 5097 2924
## Dataset 1.00 2217 2537
## Dimension 1.00 4129 3254
## Stereo:Motion 1.00 4887 2657
## Stereo:Perspective 1.00 4527 2604
## Motion:Perspective 1.00 6393 3332
## Stereo:Shading 1.00 4232 3001
## Motion:Shading 1.00 4643 3297
## Perspective:Shading 1.00 5635 3019
## Stereo:Dataset 1.00 2025 2354
## Motion:Dataset 1.00 4251 2775
## Perspective:Dataset 1.00 5492 3004
## Shading:Dataset 1.00 4885 3070
## Stereo:Dimension 1.00 2377 2667
## Dataset:Dimension 1.00 2492 2890
## Stereo:Motion:Perspective 1.00 4841 3102
## Stereo:Motion:Shading 1.00 4777 3204
## Stereo:Perspective:Shading 1.00 5092 2935
## Motion:Perspective:Shading 1.00 6211 3028
## Stereo:Motion:Dataset 1.00 4573 2764
## Stereo:Perspective:Dataset 1.00 4950 2860
## Motion:Perspective:Dataset 1.00 5356 3000
## Stereo:Shading:Dataset 1.00 5059 3090
## Motion:Shading:Dataset 1.00 5083 3290
## Perspective:Shading:Dataset 1.00 4987 3142
## Stereo:Dataset:Dimension 1.00 2114 2301
## Stereo:Motion:Perspective:Shading 1.00 5230 2580
## Stereo:Motion:Perspective:Dataset 1.00 5440 2786
## Stereo:Motion:Shading:Dataset 1.00 5032 3184
## Stereo:Perspective:Shading:Dataset 1.00 4767 2573
## Motion:Perspective:Shading:Dataset 1.00 4181 3305
## Stereo:Motion:Perspective:Shading:Dataset 1.00 3891 2759
## shape_Intercept 1.00 5674 2748
## shape_Motion 1.00 5814 2770
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
##
## Computed from 4000 by 3320 log-likelihood matrix
##
## Estimate SE
## elpd_loo -9988.5 72.3
## p_loo 114.9 6.6
## looic 19977.0 144.5
## ------
## Monte Carlo SE of elpd_loo is NA.
##
## Pareto k diagnostic values:
## Count Pct. Min. n_eff
## (-Inf, 0.5] (good) 3314 99.8% 354
## (0.5, 0.7] (ok) 5 0.2% 118
## (0.7, 1] (bad) 1 0.0% 423
## (1, Inf) (very bad) 0 0.0% <NA>
## See help('pareto-k-diagnostic') for details.
##
## Computed from 4000 by 3320 log-likelihood matrix
##
## Estimate SE
## elpd_waic -9987.9 72.2
## p_waic 114.3 6.5
## waic 19975.8 144.4
##
## 40 (1.2%) p_waic estimates greater than 0.4. We recommend trying loo instead.summary(m_brms_time_gamma_motion)## Family: gamma
## Links: mu = log; shape = log
## Formula: ResponseTime | cens(cen) ~ 0 + Intercept + Stereo * Motion * Perspective * Shading * Dataset + Stereo * Dataset * Dimension + (1 + Motion | ParticipantID)
## shape ~ 0 + Intercept + Motion
## Data: trials (Number of observations: 3320)
## Samples: 2 chains, each with iter = 4000; warmup = 2000; thin = 1;
## total post-warmup samples = 4000
##
## Group-Level Effects:
## ~ParticipantID (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 0.62 0.08 0.48 0.81 1.01 588
## sd(Motion) 0.28 0.04 0.20 0.37 1.00 1357
## cor(Intercept,Motion) -0.50 0.15 -0.75 -0.16 1.00 1400
## Tail_ESS
## sd(Intercept) 1010
## sd(Motion) 1777
## cor(Intercept,Motion) 1873
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept 2.27 0.12 2.05 2.50
## Stereo 0.37 0.05 0.27 0.47
## Motion 0.59 0.05 0.49 0.70
## Perspective 0.04 0.02 -0.00 0.08
## Shading 0.01 0.03 -0.04 0.06
## Dataset 0.17 0.05 0.07 0.27
## Dimension 0.13 0.05 0.04 0.23
## Stereo:Motion 0.38 0.04 0.30 0.46
## Stereo:Perspective 0.03 0.04 -0.05 0.11
## Motion:Perspective 0.06 0.04 -0.03 0.14
## Stereo:Shading 0.09 0.05 -0.01 0.19
## Motion:Shading 0.15 0.05 0.05 0.24
## Perspective:Shading -0.07 0.05 -0.17 0.02
## Stereo:Dataset -0.11 0.11 -0.31 0.10
## Motion:Dataset -0.01 0.06 -0.13 0.10
## Perspective:Dataset 0.03 0.04 -0.05 0.10
## Shading:Dataset 0.07 0.05 -0.03 0.17
## Stereo:Dimension -0.06 0.10 -0.26 0.15
## Dataset:Dimension 0.06 0.10 -0.14 0.25
## Stereo:Motion:Perspective -0.03 0.08 -0.19 0.14
## Stereo:Motion:Shading -0.06 0.10 -0.25 0.14
## Stereo:Perspective:Shading 0.08 0.10 -0.12 0.28
## Motion:Perspective:Shading 0.10 0.10 -0.10 0.29
## Stereo:Motion:Dataset 0.41 0.11 0.19 0.63
## Stereo:Perspective:Dataset -0.05 0.08 -0.21 0.10
## Motion:Perspective:Dataset -0.04 0.08 -0.20 0.12
## Stereo:Shading:Dataset -0.05 0.10 -0.24 0.15
## Motion:Shading:Dataset 0.05 0.10 -0.16 0.24
## Perspective:Shading:Dataset 0.01 0.10 -0.19 0.20
## Stereo:Dataset:Dimension -0.03 0.20 -0.43 0.35
## Stereo:Motion:Perspective:Shading 0.19 0.20 -0.20 0.58
## Stereo:Motion:Perspective:Dataset 0.08 0.16 -0.25 0.39
## Stereo:Motion:Shading:Dataset -0.15 0.20 -0.54 0.23
## Stereo:Perspective:Shading:Dataset -0.07 0.20 -0.47 0.32
## Motion:Perspective:Shading:Dataset 0.26 0.20 -0.14 0.66
## Stereo:Motion:Perspective:Shading:Dataset 0.26 0.39 -0.52 1.01
## shape_Intercept 1.17 0.02 1.13 1.22
## shape_Motion 0.25 0.05 0.16 0.34
## Rhat Bulk_ESS Tail_ESS
## Intercept 1.01 263 732
## Stereo 1.00 2246 2642
## Motion 1.00 874 1758
## Perspective 1.00 5648 2768
## Shading 1.00 5097 2924
## Dataset 1.00 2217 2537
## Dimension 1.00 4129 3254
## Stereo:Motion 1.00 4887 2657
## Stereo:Perspective 1.00 4527 2604
## Motion:Perspective 1.00 6393 3332
## Stereo:Shading 1.00 4232 3001
## Motion:Shading 1.00 4643 3297
## Perspective:Shading 1.00 5635 3019
## Stereo:Dataset 1.00 2025 2354
## Motion:Dataset 1.00 4251 2775
## Perspective:Dataset 1.00 5492 3004
## Shading:Dataset 1.00 4885 3070
## Stereo:Dimension 1.00 2377 2667
## Dataset:Dimension 1.00 2492 2890
## Stereo:Motion:Perspective 1.00 4841 3102
## Stereo:Motion:Shading 1.00 4777 3204
## Stereo:Perspective:Shading 1.00 5092 2935
## Motion:Perspective:Shading 1.00 6211 3028
## Stereo:Motion:Dataset 1.00 4573 2764
## Stereo:Perspective:Dataset 1.00 4950 2860
## Motion:Perspective:Dataset 1.00 5356 3000
## Stereo:Shading:Dataset 1.00 5059 3090
## Motion:Shading:Dataset 1.00 5083 3290
## Perspective:Shading:Dataset 1.00 4987 3142
## Stereo:Dataset:Dimension 1.00 2114 2301
## Stereo:Motion:Perspective:Shading 1.00 5230 2580
## Stereo:Motion:Perspective:Dataset 1.00 5440 2786
## Stereo:Motion:Shading:Dataset 1.00 5032 3184
## Stereo:Perspective:Shading:Dataset 1.00 4767 2573
## Motion:Perspective:Shading:Dataset 1.00 4181 3305
## Stereo:Motion:Perspective:Shading:Dataset 1.00 3891 2759
## shape_Intercept 1.00 5674 2748
## shape_Motion 1.00 5814 2770
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).if(REBUILD_FLAG){
trials <- trials %>%
mutate(cen = ifelse(ResponseTime > 60, "left", "none"))
m_time_gamma_motion_simple <- bf(ResponseTime | cens(cen) ~
0 + Intercept +
Stereo*Motion*Perspective*Shading*Dataset +
Stereo*Dataset*Dimension +
(1 + Motion | ParticipantID),
family = Gamma(link="log")
)
priors_time_gamma_motion_simple <- c(
prior(normal(0, 2.5), class = "b"),
prior(normal(0, 30), class = "b", coef = "Intercept"),
prior(gamma(1, 20), class = "shape"),
prior(student_t(3, 0, 10), class = "sd")
)
m_brms_time_gamma_motion_simple <<- brm(m_time_gamma_motion,
data = trials, family = Gamma(link="log"), prior = priors_time_gamma_motion,
chains = N_CHAINS, iter = N_ITER, warmup = N_WARMUP, thin = N_THIN, cores = N_CORES,
control = list(adapt_delta = DELTA, max_treedepth = TREE_DEPTH))
saveRDS(file = "rds/m_brms_time_gamma_motion_simple.rds", m_brms_time_gamma_motion_simple)
}else{
m_brms_time_gamma_motion_simple <<- readRDS("rds/m_brms_time_gamma_motion_simple.rds")
}
model_diagnostics(m_brms_time_gamma_motion_simple)## [1] "model diagnostics"
## Family: gamma
## Links: mu = log; shape = log
## Formula: ResponseTime | cens(cen) ~ 0 + Intercept + Stereo * Motion * Perspective * Shading * Dataset + Stereo * Dataset * Dimension + (1 + Motion | ParticipantID)
## shape ~ 0 + Intercept + Motion
## Data: trials (Number of observations: 3320)
## Samples: 2 chains, each with iter = 4000; warmup = 2000; thin = 1;
## total post-warmup samples = 4000
##
## Group-Level Effects:
## ~ParticipantID (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 0.62 0.08 0.49 0.80 1.00 628
## sd(Motion) 0.28 0.04 0.20 0.38 1.00 1286
## cor(Intercept,Motion) -0.51 0.15 -0.76 -0.19 1.00 1415
## Tail_ESS
## sd(Intercept) 966
## sd(Motion) 1657
## cor(Intercept,Motion) 2004
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept 2.28 0.12 2.05 2.52
## Stereo 0.37 0.05 0.27 0.47
## Motion 0.59 0.05 0.49 0.69
## Perspective 0.04 0.02 0.00 0.08
## Shading 0.01 0.02 -0.04 0.06
## Dataset 0.16 0.05 0.06 0.27
## Dimension 0.13 0.05 0.03 0.23
## Stereo:Motion 0.38 0.04 0.30 0.46
## Stereo:Perspective 0.03 0.04 -0.05 0.11
## Motion:Perspective 0.06 0.04 -0.03 0.14
## Stereo:Shading 0.09 0.05 -0.01 0.18
## Motion:Shading 0.14 0.05 0.04 0.24
## Perspective:Shading -0.07 0.05 -0.17 0.02
## Stereo:Dataset -0.10 0.11 -0.31 0.10
## Motion:Dataset -0.01 0.06 -0.13 0.10
## Perspective:Dataset 0.03 0.04 -0.05 0.10
## Shading:Dataset 0.07 0.05 -0.03 0.16
## Stereo:Dimension -0.06 0.10 -0.26 0.15
## Dataset:Dimension 0.06 0.10 -0.13 0.26
## Stereo:Motion:Perspective -0.02 0.08 -0.18 0.14
## Stereo:Motion:Shading -0.06 0.10 -0.26 0.14
## Stereo:Perspective:Shading 0.08 0.10 -0.11 0.27
## Motion:Perspective:Shading 0.10 0.10 -0.10 0.30
## Stereo:Motion:Dataset 0.41 0.12 0.18 0.64
## Stereo:Perspective:Dataset -0.05 0.08 -0.22 0.11
## Motion:Perspective:Dataset -0.04 0.08 -0.20 0.13
## Stereo:Shading:Dataset -0.05 0.10 -0.25 0.16
## Motion:Shading:Dataset 0.05 0.10 -0.14 0.24
## Perspective:Shading:Dataset 0.01 0.10 -0.18 0.19
## Stereo:Dataset:Dimension -0.04 0.20 -0.43 0.35
## Stereo:Motion:Perspective:Shading 0.19 0.20 -0.20 0.56
## Stereo:Motion:Perspective:Dataset 0.08 0.17 -0.24 0.39
## Stereo:Motion:Shading:Dataset -0.16 0.20 -0.55 0.23
## Stereo:Perspective:Shading:Dataset -0.08 0.19 -0.45 0.31
## Motion:Perspective:Shading:Dataset 0.27 0.20 -0.14 0.66
## Stereo:Motion:Perspective:Shading:Dataset 0.26 0.40 -0.50 1.06
## shape_Intercept 1.17 0.02 1.13 1.22
## shape_Motion 0.25 0.05 0.16 0.35
## Rhat Bulk_ESS Tail_ESS
## Intercept 1.00 349 527
## Stereo 1.00 2556 2653
## Motion 1.00 758 1394
## Perspective 1.00 5636 2943
## Shading 1.00 5526 3058
## Dataset 1.00 2610 2689
## Dimension 1.00 3955 3063
## Stereo:Motion 1.00 5317 3104
## Stereo:Perspective 1.00 4829 3003
## Motion:Perspective 1.00 5023 2508
## Stereo:Shading 1.00 5417 2898
## Motion:Shading 1.00 5682 2907
## Perspective:Shading 1.00 5256 3065
## Stereo:Dataset 1.00 2489 2975
## Motion:Dataset 1.00 5709 3185
## Perspective:Dataset 1.00 6050 3137
## Shading:Dataset 1.00 4946 3151
## Stereo:Dimension 1.00 2669 2968
## Dataset:Dimension 1.00 2770 2857
## Stereo:Motion:Perspective 1.00 4367 2885
## Stereo:Motion:Shading 1.00 5435 3152
## Stereo:Perspective:Shading 1.00 4465 2914
## Motion:Perspective:Shading 1.00 5049 3176
## Stereo:Motion:Dataset 1.00 5008 2769
## Stereo:Perspective:Dataset 1.00 5056 3123
## Motion:Perspective:Dataset 1.00 5304 3045
## Stereo:Shading:Dataset 1.00 5379 2716
## Motion:Shading:Dataset 1.00 4333 2781
## Perspective:Shading:Dataset 1.00 3984 3101
## Stereo:Dataset:Dimension 1.00 2661 2788
## Stereo:Motion:Perspective:Shading 1.00 4646 3093
## Stereo:Motion:Perspective:Dataset 1.00 5388 2870
## Stereo:Motion:Shading:Dataset 1.00 4071 2912
## Stereo:Perspective:Shading:Dataset 1.00 5116 2702
## Motion:Perspective:Shading:Dataset 1.00 5631 3050
## Stereo:Motion:Perspective:Shading:Dataset 1.00 5647 3238
## shape_Intercept 1.00 5217 3033
## shape_Motion 1.00 5531 2850
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
##
## Computed from 4000 by 3320 log-likelihood matrix
##
## Estimate SE
## elpd_loo -9988.0 72.2
## p_loo 114.5 6.5
## looic 19976.1 144.5
## ------
## Monte Carlo SE of elpd_loo is NA.
##
## Pareto k diagnostic values:
## Count Pct. Min. n_eff
## (-Inf, 0.5] (good) 3311 99.7% 553
## (0.5, 0.7] (ok) 8 0.2% 227
## (0.7, 1] (bad) 1 0.0% 86
## (1, Inf) (very bad) 0 0.0% <NA>
## See help('pareto-k-diagnostic') for details.
##
## Computed from 4000 by 3320 log-likelihood matrix
##
## Estimate SE
## elpd_waic -9987.4 72.2
## p_waic 113.9 6.5
## waic 19974.8 144.4
##
## 40 (1.2%) p_waic estimates greater than 0.4. We recommend trying loo instead.draw_coefs <- function(m,
target_coefs,
title = "",
fill_color = "white" ,
breaks_x = seq(0, 1, by = 0.5)
){
post_samples <- posterior_samples(m, pars = "b_")
b_CIs <- post_samples %>%
gather(key = "coefs", value = "value") %>%
group_by(coefs) %>%
median_qi() %>%
ungroup() %>%
mutate(lower95 = exp(.lower), upper95 = exp(.upper), median = exp(value))%>%
select(coefs, median, lower95, upper95) %>%
mutate(coefs = factor(coefs, levels = rev(target_coefs)),
s_lower95 = round(lower95, 3), s_upper95 = round(upper95, 3),
CIs = paste0(round(median, 3), ' [', s_lower95, ',', s_upper95, ']'))
b_samples <- post_samples %>%
gather(key = "coefs", value = "value") %>%
ungroup()
g <- b_samples %>%
filter(coefs %in% target_coefs) %>%
mutate(coefs = factor(coefs, levels = rev(target_coefs)), value = exp(value)) %>%
ggplot(aes(x = value, y = coefs)) +
stat_slab(fill = fill_color, n = (N_ITER - N_WARMUP) * N_CHAINS) +
geom_richtext(data = b_CIs, mapping = aes(x = tail(breaks_x, n = 1) * 1.1, y = coefs, label = CIs),
size = 2,
fill = NA, label.color = NA, # remove background and outline
label.padding = grid::unit(rep(0, 4), "pt")) +
geom_vline(xintercept = 1, linetype = "dashed", size = LINE_SIZE) +
scale_x_continuous(breaks = breaks_x, expand = expansion(mult = c(0.01, .5))) +
coord_cartesian(xlim = c(breaks_x[1], tail(breaks_x, n = 1))) +
ggtitle(title) + xlab("exp(beta)") + ylab("")
return(g)
}How do the six manipulated variables affect participants’ performance?
target_coefs_rq1 <- c("b_Stereo", "b_Motion", "b_Perspective", "b_Shading", "b_Dimension", "b_Dataset")
g1_rq1 <- draw_coefs(m_brms_error_hurdle_gamma,
target_coefs_rq1,
"Error magnitude (%)",
ERROR_COLOR,
breaks_x = seq(0.75, 1.5, by = 0.25))
g2_rq1 <- draw_coefs(m_brms_time_gamma_motion,
target_coefs_rq1,
"Response time (s)",
TIME_COLOR,
breaks_x = seq(0.85, 2.2, by = 0.45))
g_combined_rq1 <- ggarrange(g1_rq1, g2_rq1, ncol = 2)
ggsave(g_combined_rq1, filename = "pic/RQ1-mean-effects.pdf", width = 8, height = 2.5, units = "in")
g_combined_rq1
Interaction effects
target_coefs_rq2 <- c("b_Stereo:Motion",
"b_Stereo:Perspective",
"b_Stereo:Shading",
"b_Stereo:Dimension",
"b_Stereo:Dataset",
"b_Motion:Perspective",
"b_Motion:Shading",
"b_Motion:Dataset",
"b_Perspective:Shading",
"b_Perspective:Dataset",
"b_Shading:Dataset",
"b_Dataset:Dimension")
g1_rq2 <- draw_coefs(m_brms_error_hurdle_gamma,
target_coefs_rq2,
"Error magnitude (%)",
ERROR_COLOR,
breaks_x = seq(0.5, 2.1, by = 0.5))
g2_rq2 <- draw_coefs(m_brms_time_gamma_motion,
target_coefs_rq2,
"Response time (s)",
TIME_COLOR,
breaks_x = seq(0.5, 2.1, by = 0.5))
g_combined_rq2 <- ggarrange(g1_rq2, g2_rq2, ncol = 2)
ggsave(g_combined_rq2, filename = "pic/RQ2-interaction-effects.pdf", width = 8, height = 3.5, units = "in")
g_combined_rq2
draw_post <- function( m,
title = "",
fill_color = "white" ,
palette_in,
adjust_in,
breaks_x = seq(0, 1, by = 0.5)
){
post_samples <- trials %>%
select(Stereo, Motion, Perspective, Shading, Dimension, Dataset) %>%
distinct() %>%
add_fitted_draws(m, value = "sample_value", scale = "linear", re_formula = NA, allow_new_levels = FALSE) %>%
select(-c(".chain", ".iteration"))%>%
ungroup()%>%
select(Stereo, Motion, Perspective, Shading, Dimension, Dataset, sample_value) %>%
gather(key = "levels_names", value = "levels_values", Stereo, Motion, Perspective, Shading, Dimension, Dataset) %>%
mutate(levels_values = factor(levels_values), sample_value = exp(sample_value))
b_CIs <- post_samples %>%
group_by(levels_names, levels_values) %>%
median_qi() %>%
ungroup() %>%
mutate(lower95 = .lower, upper95 = .upper, median = sample_value)%>%
mutate(levels_values = factor(levels_values),
s_lower95 = round(lower95, 3), s_upper95 = round(upper95, 3),
CIs = paste0(round(median, 3), ' [', s_lower95, ',', s_upper95, ']'))
g <- post_samples %>%
ggplot(aes(x = sample_value, y = levels_names)) +
geom_density_ridges(
aes(fill = levels_values, color = levels_values),
rel_min_height = 0.001,
alpha = 0.5,
scale = 0.8,
size = 0.5
) +
geom_richtext(data = b_CIs, mapping = aes(x = tail(breaks_x, n = 1) * 1.2,
y = levels_names,
color = levels_values,
label = CIs),
label.color = NA,
size = 2,
fill = NA,
label.padding = grid::unit(rep(0, 4), "pt")) +
scale_x_continuous(breaks = breaks_x, expand = expansion(mult = c(0.01, .5))) +
scale_fill_manual(values = palette_in) +
scale_color_manual(values = palette_in) +
coord_cartesian(xlim = c(breaks_x[1], tail(breaks_x, n = 1))) +
ggtitle(title) + xlab("") + ylab("")
return(g)
}
g1_rq3 <- draw_post(m_brms_error_hurdle_gamma,
"Error magnitude (%)",
ERROR_COLOR,
PALETTE_ERROR,
adjust_in = 1,
breaks_x = seq(0, 15, by = 5))
g2_rq3 <- draw_post(m_brms_time_gamma_motion,
"Response time (s)",
TIME_COLOR,
PALETTE_TIME,
adjust_in = 2,
breaks_x = seq(0, 45, by = 15))
g_combined_rq3 <- ggarrange(g1_rq3, g2_rq3, ncol = 2)
ggsave(g_combined_rq3, filename = "pic/RQ3-div.pdf", width = 7, height = 3.5, units = "in")
g_combined_rq3
global_order <- NULL
draw_all <- function( m,
title = "",
fill_color = "white" ,
palette_in,
adjust_in,
breaks_x = seq(0, 1, by = 0.5),
which = "error"
){
post_samples <- trials %>%
select(Stereo, Motion, Perspective, Shading, Dimension, Dataset) %>%
distinct() %>%
add_fitted_draws(m, value = "sample_value", scale = "linear", re_formula = NA, allow_new_levels = FALSE) %>%
select(-c(".chain", ".iteration"))%>%
ungroup()%>%
select(Stereo, Motion, Perspective, Shading, Dimension, Dataset, sample_value) %>%
mutate( Stereo = recode(Stereo, `0.5` = "HMD", `-0.5` = "Desktop"),
Motion = recode(Motion, `0.5` = "Motion", `-0.5` = "No Motion"),
Perspective = recode(Perspective, `0.5` = "Perspective", `-0.5` = "Orthographic"),
Shading = recode(Shading, `0` = "Simple Shading", `0.5` = "Ambient Occlusion", `-0.5` = "Flat Shading"),
Dataset = recode(Dataset, `0.5` = "CIFAR-10", `-0.5` = "bAbI"),
Dimension = recode(Dimension, `-0.5` = "2D t-SNE", `0.5` = "3D t-SNE"),
sample_value = exp(sample_value),
Condition = paste(Stereo, Motion, Perspective, Shading, Dimension, Dataset, sep = seper))
b_CIs <- post_samples %>%
select(Condition, sample_value) %>%
group_by(Condition) %>%
median_qi() %>%
ungroup() %>%
mutate(lower95 = .lower, upper95 = .upper, median = sample_value,
s_lower95 = round(lower95, 3), s_upper95 = round(upper95, 3),
CIs = paste0(round(median, 3), ' [', s_lower95, ',', s_upper95, ']'))
if(which == "error"){
b_CIs <- b_CIs %>%
mutate(Condition = fct_reorder(Condition, .x = median, .desc = TRUE))
global_order <<- levels(b_CIs$Condition)
}else{
b_CIs <- b_CIs %>%
mutate(Condition = factor(Condition, levels = global_order))
}
g <- post_samples %>%
ggplot(aes(x = sample_value, y = Condition)) +
theme(axis.text.y = element_text(size = 3)) +
geom_richtext(data = b_CIs, mapping = aes(x = tail(breaks_x, n = 1) * 1.2,
y = Condition,
label = CIs),
label.color = NA,
size = 3,
fill = NA,
label.padding = grid::unit(rep(0, 4), "pt")) +
geom_density_ridges(
fill = fill_color,
rel_min_height = 0.01,
alpha = 0.5,
scale = 1.5,
size = 0.5
) +
scale_x_continuous(breaks = breaks_x, expand = expansion(mult = c(0.01, .5))) +
coord_cartesian(xlim = c(breaks_x[1], tail(breaks_x, n = 1))) +
ggtitle(title) + xlab("") + ylab("")
g
return(g)
}
g1_rq4 <- draw_all(m_brms_error_hurdle_gamma,
"Error magnitude (%)",
ERROR_COLOR,
PALETTE_ERROR,
adjust_in = 1,
breaks_x = seq(3, 15, by = 4),
which = "error")
g2_rq4 <- draw_all(m_brms_time_gamma_motion,
"Response time (s)",
TIME_COLOR,
PALETTE_TIME,
adjust_in = 1,
breaks_x = seq(0, 36, by = 12),
which = "time")
g_combined_rq4 <- ggarrange(g1_rq4, g2_rq4, ncol = 2)
ggsave(g_combined_rq4, filename = "pic/RQ4-all.pdf", width = 15, height = 12, units = "in")
g_combined_rq4
# Extra figures
demographics <- metas %>% select(familiarML, familiarDR, familiarVIS, familiarVR)
demographics_stack <- stack(demographics)
demographics_stack$overall <- paste(demographics_stack$values, demographics_stack$ind, sep = " ")
demographics_table <- aggregate(data = demographics_stack, values ~ overall, length)
demographics_table$item <- sapply(demographics_table$overall, function(x){return(strsplit(x, split = " ")[[1]][2])})
demographics_table$option <- sapply(demographics_table$overall, function(x){return(strsplit(x, split = " ")[[1]][1])})
g_demographics <- ggplot() %>%
+ geom_tile(data = demographics_table, aes(x = option, y = item, fill = values)) %>%
+ scale_fill_continuous(low = "#ffffff", high = ERROR_COLOR, limits = c(0,24), breaks = c(0, 8, 16, 24)) + xlab("scale") + ylab("")
g_demographics
ggsave(file = "pic/demographics.pdf", g_demographics, width = 2.7, height = 2, units = "in")Accuracy range examples
acc1 <- c(0.3978, 0.4054, 0.5998, 0.602, 0.605, 0.6052, 0.6528, 0.653, 0.6614, 0.6762, 0.6956, 0.7044, 0.713, 0.7162, 0.725, 0.73, 0.7326, 0.7362, 0.7398, 0.745, 0.7458, 0.7476, 0.751, 0.7538, 0.7668, 0.767, 0.7686, 0.7686, 0.769, 0.7744, 0.7748, 0.7754, 0.7758, 0.7778, 0.7788, 0.7794, 0.7806, 0.7828, 0.7834, 0.7848, 0.7858, 0.7882, 0.7888, 0.789, 0.7894, 0.7914, 0.7932, 0.7946, 0.7948, 0.7952, 0.7954, 0.7966, 0.7968, 0.7976, 0.799, 0.7992, 0.801, 0.8014, 0.8018, 0.8026, 0.8028, 0.8032, 0.804, 0.804, 0.8046, 0.805, 0.8056, 0.8058, 0.806, 0.8066, 0.8068, 0.8072, 0.8076, 0.808, 0.8084, 0.8098, 0.8108, 0.8108, 0.8108, 0.8118, 0.812, 0.8132, 0.8138, 0.8138, 0.8148, 0.816, 0.816, 0.8172, 0.8176, 0.8182, 0.8192, 0.8202, 0.8204, 0.8204, 0.8206, 0.8206, 0.8206, 0.8212, 0.8212, 0.822, 0.8224, 0.824, 0.8244, 0.8254, 0.8258, 0.8268, 0.8274, 0.8276, 0.8286, 0.8286, 0.829, 0.8302, 0.8314, 0.8314, 0.8326, 0.833, 0.8332, 0.8338, 0.834, 0.8352, 0.8358, 0.8364, 0.837, 0.8384, 0.8386, 0.8386, 0.8396, 0.8406, 0.8408, 0.8408, 0.8414, 0.842, 0.8428, 0.8436, 0.8442, 0.8444, 0.8444, 0.8446, 0.845, 0.8452, 0.847, 0.8472, 0.8472, 0.8474, 0.8474, 0.848, 0.85, 0.8504, 0.8506, 0.8514, 0.8516, 0.8518, 0.8534, 0.855, 0.8578, 0.858, 0.8582, 0.8584, 0.8584, 0.861, 0.8634, 0.8662, 0.8912, 0.8914, 0.8922, 0.8942, 0.8954, 0.896, 0.896, 0.896, 0.8962, 0.8964, 0.8966, 0.8968, 0.8972, 0.8974, 0.8978, 0.8978, 0.8978, 0.8982, 0.8982, 0.8984, 0.8984, 0.8986, 0.899, 0.8992, 0.8992, 0.8994, 0.8996, 0.8998, 0.8998, 0.8998, 0.8998, 0.8998, 0.9, 0.9, 0.9002, 0.9002, 0.9002, 0.9002, 0.9002, 0.9004, 0.9006, 0.9006, 0.9008, 0.901, 0.901, 0.9012, 0.9012, 0.9014, 0.9014, 0.9014, 0.9016, 0.9018, 0.9018, 0.9018, 0.902, 0.902, 0.902, 0.9022, 0.9024, 0.9026, 0.9026, 0.9026, 0.9026, 0.9026, 0.9028, 0.9028, 0.903, 0.903, 0.903, 0.903, 0.903, 0.9032, 0.9032, 0.9036, 0.9036, 0.9036, 0.9036, 0.9036, 0.9038, 0.9038, 0.9038, 0.9038, 0.9044, 0.9044, 0.9044, 0.9044, 0.9046, 0.9046, 0.905, 0.9052, 0.9052, 0.9052, 0.9054, 0.9054, 0.9056, 0.9056, 0.9056, 0.9058, 0.9058, 0.9058, 0.9058, 0.906, 0.906, 0.906, 0.906, 0.906, 0.9062, 0.9064, 0.9064, 0.9066, 0.9066, 0.9068, 0.9068, 0.9068, 0.9068, 0.907, 0.907, 0.9074, 0.9074, 0.9074, 0.908, 0.908, 0.9086, 0.9092, 0.9092, 0.9092, 0.9092, 0.9094, 0.9094, 0.9098, 0.9098, 0.91, 0.9106, 0.9114, 0.9114, 0.9126, 0.913, 0.9146)
acc2 <- c(0.192, 0.246, 0.394, 0.405, 0.427, 0.439, 0.476, 0.485, 0.488, 0.488, 0.49, 0.491, 0.491, 0.492, 0.492, 0.494, 0.496, 0.496, 0.497, 0.497, 0.497, 0.498, 0.498, 0.499, 0.499, 0.499, 0.5, 0.5, 0.5, 0.5, 0.5, 0.501, 0.504, 0.505, 0.505, 0.506, 0.506, 0.507, 0.507, 0.508, 0.508, 0.508, 0.508, 0.509, 0.509, 0.51, 0.51, 0.511, 0.511, 0.512, 0.512, 0.514, 0.515, 0.515, 0.515, 0.516, 0.522, 0.526, 0.53, 0.531, 0.531, 0.531, 0.534, 0.542, 0.548, 0.559, 0.564, 0.6, 0.625, 0.658, 0.681, 0.697, 0.722, 0.724, 0.726, 0.731, 0.735, 0.739, 0.739, 0.739, 0.739, 0.743, 0.747, 0.748, 0.753, 0.762, 0.764, 0.767, 0.776, 0.79, 0.79, 0.792, 0.795, 0.802, 0.803, 0.81, 0.813, 0.813, 0.817, 0.819, 0.82, 0.82, 0.823, 0.824, 0.824, 0.826, 0.828, 0.828, 0.834, 0.837, 0.838, 0.839, 0.841, 0.841, 0.842, 0.842, 0.843, 0.843, 0.844, 0.847, 0.848, 0.852, 0.853, 0.854, 0.854, 0.854, 0.856, 0.857, 0.857, 0.857, 0.859, 0.86, 0.862, 0.863, 0.863, 0.864, 0.865, 0.866, 0.871, 0.871, 0.874, 0.874, 0.875, 0.876, 0.879, 0.88, 0.881, 0.883, 0.883, 0.883, 0.884, 0.886, 0.886, 0.886, 0.887, 0.887, 0.888, 0.891, 0.891, 0.893, 0.893, 0.894, 0.896, 0.896, 0.896, 0.897, 0.898, 0.899, 0.901, 0.901, 0.901, 0.901, 0.902, 0.903, 0.904, 0.904, 0.904, 0.905, 0.905, 0.905, 0.907, 0.908, 0.908, 0.909, 0.91, 0.91, 0.91, 0.911, 0.911, 0.911, 0.911, 0.912, 0.912, 0.913, 0.913, 0.914, 0.917, 0.917, 0.92, 0.922)
acc3 <- c(0.838, 0.839, 0.8405, 0.8505, 0.8575, 0.8575, 0.865, 0.872, 0.872, 0.873, 0.8735, 0.8745, 0.882, 0.882, 0.8835, 0.885, 0.8865, 0.887, 0.887, 0.892, 0.892, 0.8935, 0.895, 0.8955, 0.896, 0.897, 0.8975, 0.898, 0.898, 0.8985, 0.8985, 0.899, 0.8995, 0.8995, 0.8995, 0.9, 0.9015, 0.902, 0.9025, 0.9035, 0.904, 0.9045, 0.9045, 0.905, 0.9055, 0.9055, 0.906, 0.906, 0.9075, 0.908, 0.9085, 0.9085, 0.9085, 0.9085, 0.9095, 0.9095, 0.9105, 0.9105, 0.9105, 0.911, 0.9115, 0.9115, 0.9115, 0.9115, 0.9125, 0.9125, 0.9125, 0.9125, 0.9125, 0.9125, 0.913, 0.9135, 0.9135, 0.9135, 0.914, 0.914, 0.914, 0.9145, 0.915, 0.915, 0.915, 0.9155, 0.9155, 0.9155, 0.9155, 0.916, 0.916, 0.916, 0.9165, 0.9165, 0.917, 0.917, 0.917, 0.917, 0.9175, 0.918, 0.918, 0.918, 0.918, 0.918, 0.918, 0.918, 0.9185, 0.9185, 0.9185, 0.9185, 0.9185, 0.919, 0.919, 0.919, 0.9195, 0.9195, 0.9195, 0.9195, 0.9195, 0.9195, 0.9195, 0.9195, 0.9195, 0.9195, 0.92, 0.92, 0.92, 0.92, 0.9205, 0.9205, 0.9205, 0.9205, 0.921, 0.921, 0.9215, 0.9215, 0.9215, 0.9215, 0.9215, 0.922, 0.922, 0.922, 0.922, 0.922, 0.922, 0.9225, 0.9225, 0.9225, 0.9225, 0.923, 0.923, 0.923, 0.923, 0.9235, 0.9235, 0.9235, 0.9235, 0.9235, 0.9235, 0.924, 0.924, 0.924, 0.924, 0.9245, 0.9245, 0.9245, 0.9245, 0.9245, 0.9245, 0.9245, 0.9245, 0.925, 0.925, 0.925, 0.925, 0.9255, 0.9255, 0.9255, 0.9255, 0.9255, 0.9255, 0.9255, 0.9255, 0.926, 0.926, 0.926, 0.926, 0.926, 0.9265, 0.9265, 0.927, 0.927, 0.927, 0.927, 0.927, 0.927, 0.927, 0.927, 0.927, 0.9275, 0.9275, 0.9275, 0.9275, 0.928, 0.928, 0.928, 0.928, 0.928, 0.928, 0.928, 0.928, 0.9285, 0.9285, 0.9285, 0.9285, 0.9285, 0.9285, 0.929, 0.929, 0.929, 0.929, 0.929, 0.929, 0.9295, 0.9295, 0.93, 0.93, 0.93, 0.93, 0.93, 0.9305, 0.9305, 0.9305, 0.931, 0.9315, 0.9315, 0.9315, 0.9315, 0.932, 0.9325, 0.9325, 0.933, 0.9335, 0.9335, 0.9335, 0.934, 0.9345, 0.9345, 0.936, 0.936, 0.937, 0.937, 0.94, 0.9405)
g_bar1 <- ggplot() %>%
+ geom_linerange(aes(ymax = 1, ymin = 0, x = acc1), alpha = 0.2, color = ERROR_COLOR) %>%
+ scale_x_continuous(limits=c(0,1), breaks = seq(0, 1, by = 0.1), expand=c(0,0))%>%
+ scale_y_continuous(limits=c(0,1), breaks = seq(0, 1, by = 1), expand=c(0,0))
g_bar2 <- ggplot() %>%
+ geom_linerange(aes(ymax = 1, ymin = 0, x = acc2), alpha = 0.2, color = ERROR_COLOR)%>%
+ scale_x_continuous(limits=c(0,1), breaks = seq(0, 1, by = 0.1), expand=c(0,0))%>%
+ scale_y_continuous(limits=c(0,1), breaks = seq(0, 1, by = 1), expand=c(0,0))
g_bar3 <- ggplot() %>%
+ geom_linerange(aes(ymax = 1, ymin = 0, x = acc3), alpha = 0.2, color = ERROR_COLOR)%>%
+ scale_x_continuous(limits=c(0,1), breaks = seq(0, 1, by = 0.1), expand=c(0,0))%>%
+ scale_y_continuous(limits=c(0,1), breaks = seq(0, 1, by = 1), expand=c(0,0))
g_bars <- ggarrange(g_bar1, g_bar2, g_bar3, ncol = 1, align="v")
ggsave(file = "pic/acc_bar.pdf", g_bars , width = 4, height = 1.6, units = "in")